A brute-force approach assuming that the solution is a whole number, and I
am understanding the problem correctly, follows after a few blank lines...


























   ((0 = -/ .*@:(2 2$21 38 55 106 - ])"0) # ]) i.111
4

Checking,

   -/ .* (2 2$21 38 55 106 - 4)
0

Indeed, 17 is a common factor.  Actually,

   +./ 21 38 55 106 - 4
17

On Tue, Aug 14, 2018 at 2:07 AM, Skip Cave <s...@caveconsulting.com> wrote:

> Attempting to solve the following Quora problem:
>
> What number must be subtracted from 21, 38, 55, and 106 each so that the
> remainders (technically differences) are proportional?
>
> Subtract the integers 0-9 from all four integers in the problem. Then find
> the prime factors of each set of four integers. Finally look for columns
> that have common factors in all four results:
>
> ]b=.q: each 21 38 55 106-/a=.i.10
>
> ┌────┬───────┬────────┬──────┬──────┬───────┬─────────┬─────
> ────┬─────┬─────┐
>
> │3 7 │2 2 5 │19 │2 3 3 │17 │2 2 2 2│3 5 │2 7 │13 │2 2 3│
>
> ├────┼───────┼────────┼──────┼──────┼───────┼─────────┼─────
> ────┼─────┼─────┤
>
> │2 19│37 │2 2 3 3 │5 7 │2 17 │3 11 │2 2 2 2 2│31 │2 3 5│29 │
>
> ├────┼───────┼────────┼──────┼──────┼───────┼─────────┼─────
> ────┼─────┼─────┤
>
> │5 11│2 3 3 3│53 │2 2 13│3 17 │2 5 5 │7 7 │2 2 2 2 3│47 │2 23 │
>
> ├────┼───────┼────────┼──────┼──────┼───────┼─────────┼─────
> ────┼─────┼─────┤
>
> │2 53│3 5 7 │2 2 2 13│103 │2 3 17│101 │2 2 5 5 │3 3 11 │2 7 7│97 │
>
> └────┴───────┴────────┴──────┴──────┴───────┴─────────┴─────
> ────┴─────┴─────┘
>
>
> Now how can I write a J function that lists the column index in this array
> where all four sets of factors have at least one common factor?  Spoiler -
> In the example, the 5th set (column index 4) has a common factor of 17.
>
>
> Skip
>
>
> Skip Cave
> Cave Consulting LLC
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